A self-study Russian mathematician, kicked out 3 times in high schools, expelled from Moscow University, all because he did not attend classes, preferred to self-study in a broader scope for his curiosity, at his own faster speed than the rigid curriculum and boring test-and-exams regime in classrooms.
He did the PhD in Harvard by invitation even he did not have a Bachelor degree, and he barely passed the Harvard’s QE (Qualifying Exams) in Algebraic Geometry, a field in which he made a revolutionary discovery few years later, and for which he was awarded the highest honor : Fields Medal.
This is the typical trait of the geniuses like Evariste Galois, Albert Einstein, Ramanujian, Hua Luogeng (华罗庚), Zhang YiTang (张益唐 – proved “70m Twin Prime Gap”) [#] , Chen Jingrun (陈景润, proved Goldbach Conjecture “1+2”) [##]… with self-motivated curiosity in their field of passion, with reading from the Masters’ works by themselves, PLUS thinking on a problem over many years with perseverance, they finally made great discoveries !
- Topology 拓扑
- Algebraic Geometry 代数几何: Geometry and Algebraic Equations
- Motif: Grothendieck
- Homotopy Theory 同伦
[Full Article] :
[#] : https://tomcircle.wordpress.com/2014/03/01/gaps-between-primes-zhang-yitang/
[##] : https://tomcircle.wordpress.com/2015/07/24/goldbach-conjecture-theorem-chen/
Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic equations.
The “Story-Telling” memory technique via “Signposts” can be used to reconstruct math from first principles:
Note: Lewis Carroll: the author of “Alice in wonderland”
Cambridge Professor Tim Gowers (Fields Medalist) suggested the similar pedagogy of “Memorise by First Principles”.
What is Math ? Interesting article below:
- Mathematics = “that which is learned“ –(Pythagoras)
Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)…
What is Axiom, Lemma, Proposition ? Why rigorous Calculus was needed hundred years after Newton & Leibniz had invented it – “Epsilon-Delta” Analysis.
Difference between Riemann Integral & Lebesgue Integral ?
Case “=” : if (a, b) independent
Case “>” : if (a, b) dependent
Thomas Royen used only high-school math (function, derivative) in his proof in 2014. He then published it in arxiv.org website – like Perelman did with the “Poincaré Conjecture”.
Russian Jewish mathematician Grigori Perelman proved the Poincaré Conjecture in 7 years of solitude research in his Russian apartment – same 7 years of solitude for Andrew Wiles (The Fermat’s Last Theorem) in the Cambridge attic house and Zhang Yitang 张益唐 (7-Million-Gap Twin Primes) in the “Subway” sandwich kitchen.
7 is the Perfect Number. 1 week has 7 days, according to the “Book of Genesis”, God created the universe in 6 days and rested “Sabbath” on the beautiful 7th day.
People involved in his journey:
His mother who supported his early education in Math, all the way to his international fame and adulthood — Erdös Paul also had a mother supporting her single son in the entire Mathematical life.
Prof Hamilton who “unintentionally” gave him the inspiration of the “Ricci-flow” tool – the first key to the door of The Poincaré Conjecture.
His closed Chinese friend the MIT Math Prof 田刚 (Tian Gang) – a PhD student of Prof S.T. Yau.
Fields Medal which he rejected — reason being he felt Prof Hamilton deserved a share of the credit.
Clay Prize which he rejected the U$ 1 million — for the same reason as the Fields Medal.
Prof S.T. Yau (邱成桐) ‘s lawsuit against “The New Yorker” jounalists on “The Poincaré Conjecture” article regarding the purported claims by his 2 Chinese mathematician students.